Problem: Simplify the following expression: $6\sqrt{175}$.
First, try to factor a perfect square out of the radical. $= 6\sqrt{175}$ $= 6\sqrt{25 \cdot 7}$ Separate the radical and simplify. $= 6\sqrt{25} \cdot \sqrt{7}$ $= 6 \cdot 5 \cdot \sqrt{7}$ $= 30\sqrt{7}$